Hello, and welcome to Christianity Stack Exchange. You may like to check out our tour information page and find out about what "tags" are and how to use them. Your question does not have anything to do with Israel, so please allow me to change that for you in order to attract relevant answers: christianity.stackexchange.com/tour
– LesleyJun 26 '18 at 16:27

My mistake - of course this subject has to do with Israel! Tag returned.
– LesleyJun 26 '18 at 16:44

Replacement theology is a term usually used by those who hold to the eschatological position known as dispensational premillenialism. It is defined as the teaching that the Church has replaced Israel, hence, "replacement" theology. However, it is usually used as a mischaracterisation of covenant theology.

Covenant theology, in the context of the ARPC, is the teaching that God has dealt with humanity through two overarching covenants: the Covenant of Works, and the Covenant of Grace. The Biblical covenants (e.g. Adamic, Noahic, Mosaic, Davidic, New) fall within the categories of the Covenant of Works or the Covenant of Grace. The ARPC subscribes to covenant theology, as defined in their doctrinal statements found in the Westminster Standards. For example, in the Westminster Confession of Faith, Chapter 7 describes God's covenants with man.

Covenant theology teaches that the church is the new Israel, and that all of the elect throughout history are members of the church. This means that the believers during the Old (Mosaic) Covenant, who were citizens of the nation of Israel, are members of the church. As such, there is not a strong distinction between Israel and the church in covenant theology.

Dispensational premillenials typically miscategorise this as replacement theology, but covenant theology doesn't teach that the church replaced Israel, but that the church is Israel. This is supported by passages such as Romans 4:16-17, and Romans 9:6-7. This does depend on Israel being understood not as a physical nation primarily, but rather as a spiritual nation, comprised of the spiritual children of Abraham by faith, namely, the church.

So the ARPC does not subscribe to replacement theology, but many dispensational premillenials will say that it does based on their understanding of ARPC theology.

Your other two questions should probably be in another question, and I can answer them if you ask them as new questions.